A circle is defined as a set of all such points
in a given plane which lie at a fixed distance from a fixed point
in the plane. This fixed point is called the center of the
circle and the fixed distance is called the radius of the
circle (see figure 7.1).

Figure 7.1

Figure 8.1 shows a circle where point P is
the center of the circle and segment PQ is known as the radius.
The radius is the distance between all points on the circle and
P. It follows that if a point R exists such that l (seg.PQ) >
l (seg.PR) the R is inside the circle. On the other hand for a point
T if l (seg.PT) > l (seg.PQ) T lies outside the circle. In figure
8.1 since l (seg.PS) = l (seg.PQ) it can be said that point S lies
on the circle.